BTW: If you are simply having trouble remembering which of the angles in the small triangle is the same as $\alpha$, imagine that there is hinge at the joint and let $\alpha$ get small...
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dmckee♦Jul 17 '11 at 13:23

2 Answers
2

Angles with their sides perpendicular are always equal. In the present example the arrow of $\vec{F}_1$ is perpendicular to the baseline, and the longest dotted line is perpendicular to the incline.

You can just imagine rotating one of the two triangles to put it on top of the other. Since the sides start off perpendicular, after a 90-degree rotation they will align, and hence show you that the angles are equal.